Math  /  Calculus

QuestionConsider the following theorem. Theorem If ff is integrable on [a,b[a, b ], then abf(x)dx=limni=1nf(xi)Δx\int_{a}^{b} f(x) d x=\lim _{n \rightarrow \infty} \sum_{i=1}^{n} f\left(x_{i}\right) \Delta x where Δx=ban\Delta x=\frac{b-a}{n} and xi=a+iΔxx_{i}=a+i \Delta x. Use the given theorem to evaluate the definite integral. 15(x24x+5)dx\int_{1}^{5}\left(x^{2}-4 x+5\right) d x

Studdy Solution
The definite integral is 403\frac{40}{3}.

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